There are numerous publications in which open spectral
gaps are detected due to high-contrast of coefficients in differential
operators or shape irregularities of the periodicity cells, see
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} and
[9]}, [10]}, [11]}, [12]}, [13]} among others. Such singular perturbations
often provide disintegration of the periodicity cells in the limit
and, as a result, the appearance of sufficiently wide gaps in the low-
and/or middle-frequency ranges of the spectrum. Both variational
and asymptotic methods have been employed in the cited papers to
detect and describe those gaps.
